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7. How to Draw Tessellations of the Escher Type

How to Draw Tessellations of the Escher Type by Joseph L. Teeters. Mathematics Teacher April 1974. 307-310



Teeters states in the subtitle and introduction:

A short, clear discussion showing how you or your students can create tessellation art

and

The writer presents here a technique that has proved useful in creating fundamental regions of the Escher type...

If only! Unfortunately, the article does the exact opposite! It’s unstructured, unclear, overblown, the pictures lack captions/titles and has tessellations appearing without explanation or reference in the text, resulting in a veritable mess. The ‘procedure’ explanation given is unnecessarily convoluted and unclear, and of what it is referring to as well – the unicyclist accompanying it? Indeed, even after looking at this several times since I began doing tessellation, it remains obscure. To try and unravel this is a veritable nightmare. Has anyone actually tried these techniques? Let me know if so.

Critiques:

1. Unicyclist, page 307
A better tessellation. Of its type quite pleasing, in that it does indeed bear a resemblance to a unicyclist, and as it is of a less frequently occurring type of motif (indeed, it is unique), this is worthy of more praise than of more common motifs.

2. St Bernard Dog, page 309
A better tessellation. A reasonable portrayal of a dog is shown, and more specifically of a specific breed as well, with the pleasing factor of a rum barrel beneath the Saint Bernard’s collar adding to the interpretation. However, the position adopted is not a true representation of a sitting dog (if this interpretation is correct), albeit this is masked to some extent by the relative quality of the interior elements.

3. Red Indian with Tomahawk, page 310
A better tessellation. A reasonable portrayal of a Red Indian is shown, and more specifically accompanied by appropriate dress, thereby reinforcing the tessellation. However, there are no instructions as to how Teeters constructed this.

Summary

A distinct dichotomy exists here, in that the instructions are obscure, of no practical use. However, in contrast, the three tessellations are all of relative quality.

Last updated: 29 March 2010

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